This invention pertains to the field of measurement of fluid flowrate.
Among the many techniques for measuring flowrate are those which measure a pressure or pressure difference and then determine flowrate by means of a relationship between that measured pressure and flowrate. Pressure measurements can be measurements at a point (such as a pitot tube), measurements along a line (such as a pitot bar or averaging pitot tube), or measurements which involve the entire flow. The last category of the three categories, i.e., measurements which involve the entire flow, is termed obstruction type flowmeters.
Obstruction type flowmeters are themselves conventionally subdivided into the following three types: orifices, venturis, and nozzles, as described in many basic fluid mechanics texts such as xe2x80x9cFluid Mechanicsxe2x80x9d by Frank White. An orifice is a calibrated opening, usually sharp-edged, of smaller open area than the duct in which it is placed. A pressure drop, which is irrecoverable, exists across the orifice and this pressure drop is also the signal which is measured to indicate the flow. A nozzle is similar to an orifice in that the measured pressure signal is the irrecoverable pressure drop, but the nozzle is more smoothly contoured than an orifice and so produces a smaller irrecoverable pressure drop, if all other parameters are comparable. Finally, a venturi also employs a contraction to an area smaller than the duct in which it is placed, but it has a region of smooth contouring both upstream and especially downstream of the minimum area, in order to reduce the irrecoverable pressure drop. The pressure signal from a venturi is taken by placing one pressure tap at the wall of the minimum-area passage and another pressure tap upstream or downstream at the full-area duct, and taking the difference between those two readings. In contrast to the orifice and nozzle, the pressure signal from a venturi is due mainly to the change in static pressure between the faster-moving fluid at the minimum area and the slower-moving fluid elsewhere. A venturi of course has some irrecoverable pressure drop, but the pressure signal from a venturi is larger, often many times larger, than the irrecoverable pressure drop.
All of these obstruction type flowmeters are most commonly used in a range which is termed turbulent flow or, if not fully turbulent, at least transition flow. As described by the Reynolds number (which is defined as density*velocity*characteristic dimension which would be the minimum diameter of the orifice nozzle or venturi, divided by the viscosity of the fluid), this would be a Reynolds number above approximately 10000. In these flowmeters the relationship between the pressure signal (measured pressure difference) and flowrate is generally quadratic or almost quadratic, i.e., deltap=C*flowrate{circumflex over ( )}n where n is approximately 2. In fact, in calibrating or describing obstruction type flowmeters, the governing relation between pressure signal and flow is usually quoted as deltap=C*flowrate{circumflex over ( )}2, and any departure from that perfectly quadratic relationship is absorbed into a secondary dependence of the proportionality constant C on Reynolds number and perhaps other quantities such as area ratio.
In the design and selection of flowmeters, an important consideration is the so-called turndown ratio, which is the ratio between the maximum and minimum flowrates measurable with the device. A flowmeter with a larger turndown ratio is more versatile and useful than a flowmeter with a smaller turndown ratio. Basically, the turndown ratio for obstruction type flowmeters derives from the fact that any pressure measuring technology has its own range limitation which is similar to a turndown ratio, that is, the usable range of maximum to minimum values of pressure which are measurable with a given accuracy. The maximum measurable pressure difference is determined by the structural limitation of the diaphragm or similar element within the pressure transducer. The minimum pressure difference is determined by considerations of signal-to-noise ratio and desired accuracy. Because of the quadratic or nearly quadratic relation between pressure signal and flowrate, an obstruction type flowmeter does not achieve an especially large turndown ratio for a given ratio of measurable pressures. For example, for traditional orifices nozzles and venturis, achieving a turndown ratio of 10 in flow measurement requires measuring pressures ranging by a factor of 100. Achieving a turndown ratio of 100 in flow measurement requires pressure measurements differing by a factor of 10000. With a single pressure transducer, achieving a pressure reading ratio of 100 is marginally possible and achieving a pressure reading ratio of 10,000 is virtually impossible. The resulting small turndown ratio is one of the significant disadvantages of obstruction type flowmeters. It may be possible to use two pressure measuring devices of different range if the more sensitive device can be exposed to some degree of overpressure (pressure larger than its design range for measuring) without being damaged, but the limitations of the quadratic relationship are still clearly evident. A flowrate-pressure relationship with an exponent of less than 2 would be desirable in order to enable a larger turndown ratio in flow measurements.
The flowmeter of the present invention does not necessarily operate in the laminar flow regime. However, for sake of comparison, it is also useful to discuss here the laminar flow regime. A classical result is that pressure drop is linearly proportional to flowrate, for the situation of fully-developed laminar flow. This means that the exponent of the pressure drop vs. flowrate relationship is 1, which would be attractive for a flowmeter in those circumstances in which it can be achieved. The geometries for which this derivation is most commonly presented are circular tubes and parallel plates. The restriction about laminar flow implies a low Reynolds number. The restriction about fully-developed flow implies a long flow passage, with the pressure drop or velocity profile being observed sufficiently far away from the entrance region, or else with the overall length being long compared to the entrance region so that the principal behavior is that of the fully-developed flow. Flowmeters are commercially available using a laminar flow element, which is an array of many tubes or flow passages of constant cross sectional area which are fluid mechanically in parallel with each other. In order to meet the restrictions of laminar and fully-developed flow, laminar flow elements are designed with a substantially large L/D (D being the diameter of an individual flow passageway, or an effective diameter if the geometry is non-circular), and effort is made to stay at a Reynolds number which is well within the laminar range. For example, literature from Meriam Co., Cleveland Ohio, one of the commercial suppliers of laminar flow elements, recommends use of the devices only at Reynolds numbers below 300. The pressure drop in the use of Meriam""s devices is measured across the entire laminar flow element including the entrance region, which is done on the assumption that the overall length of the laminar flow element is much longer than the length of the entrance (developing flow) region. In another design of laminar flowmeter, U.S. Pat. No. 5,511,416 recommends a maximum Reynolds number of 2000 or preferably 1000 and adjusts the number of available flow passages or flow area to maintain laminar flow by staying below that Reynolds number. In U.S. Pat. No. 5,837,903, Weigand, with respect to a traditional laminar flow element having a large L/D and intending to operate at low Reynolds number, notes and curve-fits a nonlinearity but carefully remains within the laminar flow regime as described exactly or with only slight corrections by the Hagen-Poiseuille Law. In general the literature pertaining to this geometry teaches away from using this geometry for flow measurement at any Reynolds number above the strictly laminar range, i.e., a Reynolds number of several hundred or at most one to two thousand, because if the flow is not strictly laminar the relationship of pressure drop vs. flowrate is not as simple as for the case of strictly laminar flow. Also, the literature pertaining to this geometry teaches that the effect of the entrance region must be minimized by making the laminar flow element so long that the entrance region is only a small fraction of the overall length. The problem with complying with these teachings of the literature about laminar flow elements is that for many flows of practical interest, the laminar flow element would have to become quite large. It becomes large in cross-section in order to reduce the velocity to a small enough value to meet the Reynolds number restriction, and it is long in order to meet the requirement for L/D of a passageway. It then would also need a substantial size of transition region to go from a possibly turbulent pipe section to a large enough cross-sectional area to produce low velocity laminar flow, followed by a similar transition back to the original cross-sectional area.
Accordingly, it is an object of the invention to provide a flowmeter based on pressure measurements, such that a larger flowrate turndown ratio is obtainable than is obtained from conventional orifices, nozzles or venturis, for a given pressure measurement ratio.
It is further an object of the invention to accomplish this without the problems of large size which are associated with a conventional laminar flow element. It is further an object of the invention to accomplish this in a way which can be used at larger Reynolds numbers than can conventional laminar flow elements. It is further an object of this invention to develop a geometry of flow obstruction element for which the pressure drop vs. flowrate relationship has an exponent smaller than 2 at Reynolds numbers larger than those traditionally associated with laminar flow.
Finally, it is an object of the invention in one embodiment to combine this invention with a variation of cross-sectional flow area to obtain a still further reduction in the steepness of the relation between the measured pressure quantity and the flowrate.
This invention is the use of a flow geometry resembling a laminar flow element, i.e., an array of surfaces or passages all of which are substantially parallel to each other and to the general flow direction, but this invention is the use of this geometry at Reynolds numbers which can extend substantially higher than the Reynolds number limitation traditionally taught, and without necessarily adhering to the traditionally taught requirement of long L/D. It has been found that for this geometry at Reynolds numbers higher than traditionally taught, the flowrate vs. pressure drop characteristics are repeatable to good accuracy, and the exponent in the pressure drop vs. flowrate relationship undergoes a smooth, gradual transition from 1 to nearly 2. It is further found that the range over which this transition occurs is so wide (several orders of magnitude in Reynolds number) that this phenomenon provides a substantial range of less-than-quadratic relationship, and it is advantageous to operate in this range which in the past has often been avoided. As a result, it is possible to create a flowmeter operating in this regime whose turndown ratio is larger than previously achievable, for a given pressure measurement ratio. In this regime the relationship between pressure drop and flowrate is not linear as would be the case in laminar flow. However, the relationship is consistent and repeatable and is sufficiently gentler than quadratic that it is worthwhile to use this geometry because it improves the achievable turndown ratio compared to existing obstruction type flowmeters. Various geometries are possible to achieve this including flat plates, honeycomb and others described herein. This invention is essentially a fourth major category of obstruction type flowmeter for turbulent flow, in addition to the orifices, nozzles and venturis already in use.
A further embodiment of this invention deals with the placement of the pressure taps at regions of unequal area, which may be acceptable in some applications. In this embodiment the pressure drop across the flow resistance element has the characteristics just described, but the pressure difference measured to indicate flow has a relationship of measured pressure vs. flowrate which is somewhat gentler than the overall pressure drop.